Evolution of circular shear layers

The Kelvin-Helmholtz instability is a generic pathway for the formation of coherent vortical structures in plasmas and ordinary fluids. Experiments have demonstrated bifurcation sequences accompanied by topological changes in the distribution of the coherent structures and various oscillating, quasi-periodic or chaotic states. Analytical and numerical studies demonstrate that such transitions can be accurately described by reducing the system of slightly viscous, forced Navier-Stokes equations to a system of ordinary differential equations of few degrees of freedom. In conjunction with these analytical calculations a highly accurate spectral code has been used to directly simulate the forced circular shear flows. Both the analytical and numerical results are in good agreement with fluid and plasma experiments. The two approaches supplement each other in predicting the transition to states of ever increasing complexity.